I have a van dedicated to my business since many of my projects require a lot gear beyond just the photography stuff. Parking, tolls, etc, are all included in my costs, but not specifically shown on the invoices. For assignments when I don't require a lot of gear, such as editorial portraits for magazines, I have a ThinkTank Airport roller bag which carries two bodies, lenses, 4 580EX strobes, pocket wizards, filters, etc, and another long bag that hold the lighting stands, grip, gels, and a couple of softboxes and reflectors. I can get around on the subway quite well with these without much hassle, and it has everything I'd need for a simple portrait. But I rarely take public transportation since its just easier and more convenient to drive.
If you really need to use public transportation, you should be able to put together a god setup in a roller bag for gear, and a medium tripod bag for stands, etc, with little trouble. Attach the tripod bag to the roller bag and its very easy to get around without any weight on your shoulders.